R-Squared – Meaning, Formula, Interpretation and Use in Mutual Funds

In summary

R-squared, or R², is the coefficient of determination used to assess how closely a fund's historical movements are associated with its benchmark. It ranges from 0% to 100%. A higher value indicates that a greater proportion of the fund's variation is explained by the benchmark, while a lower value suggests greater divergence.

• R-squared is a measure of benchmark relationship, not investment quality.
• A value of 100% indicates that the model explains all observed variation.
• A high value can be useful when assessing passive or index funds.
• A lower value can indicate greater deviation from the benchmark.
• R-squared should be assessed alongside alpha, beta, and standard deviation.
• Historical R-squared does not predict future fund behaviour.

The appropriate R-squared depends on the fund's objective. A high value may be desirable for an index fund but less informative when assessing an actively managed fund seeking differentiated returns.

R-squared is a statistical measure that indicates how much of the variation in one variable can be explained by another variable or set of variables in a regression model.

In mutual fund analysis, it is commonly used to assess how much of a fund's historical return variation is explained by its benchmark index. It is expressed as a percentage between 0% and 100%.

For example, an R-squared of 90% indicates that 90% of the variation in the fund's returns is explained by the benchmark within the specified model and observation period. It does not mean that 90% of the fund's returns came from the benchmark.

The result depends on the benchmark selected, the return data used, and the period analysed.

R-squared is closely related to correlation when a simple regression with one benchmark is used. In that setting:

R² = (Correlation between fund and benchmark)² × 100

Suppose the correlation between a fund and its benchmark is 0.90:

R² = (0.90)² × 100 = 81%

An 81% R-squared means that 81% of the variation in the fund's returns is explained by variation in the benchmark under that model. The remaining variation is associated with other factors and unexplained residuals.

Most investors do not need to calculate R-squared manually because it may be available in mutual fund factsheets and fund platforms.

R-squared is generally interpreted on a scale from 0% to 100%.

Last updated: October 2026

These ranges are indicative, not universal thresholds. The appropriate interpretation depends on the fund's investment objective and benchmark.

A high R-squared can be expected for an index fund because its objective is to closely follow a benchmark. For an actively managed fund, a high value may indicate that its historical movements have been strongly aligned with the benchmark.

No. R-squared is not a quality score.

For a passive fund, a high R-squared can support the conclusion that the fund is closely aligned with its benchmark. For an active fund, a lower value may indicate greater differentiation from the benchmark, although this does not automatically mean better performance.

For example, a fund with an R-squared of 95% and another with 65% cannot be ranked simply by comparing those figures. The first may suit an investor seeking benchmark-like exposure, while the second may reflect a more differentiated strategy.

R-squared can provide context when assessing whether a fund's historical performance should be compared closely with its benchmark.

Suppose two equity funds each report positive alpha. If one has a high R-squared against an appropriate benchmark, the benchmark provides a stronger basis for interpreting the fund's relative performance. A lower R-squared indicates that the benchmark explains less of the fund's variation, so alpha and other benchmark-relative measures need to be interpreted more carefully.

This does not establish that the fund manager has generated skill-based returns. The benchmark must also be appropriate, and performance should be considered over a meaningful period.

Correlation and R-squared are related but answer different questions.

Correlation measures the direction and strength of the linear relationship between two variables. It ranges from -1 to +1.

R-squared is the square of the correlation in a simple one-variable regression. It indicates the proportion of variation explained by the benchmark.

For example, a correlation of +0.90 and -0.90 both produce an R-squared of 81%. R-squared therefore does not tell you whether the fund and benchmark generally move in the same or opposite direction.

Beta measures the sensitivity of a fund's returns to movements in its benchmark. R-squared measures how much of the fund's return variation is explained by that benchmark.

Consider a fund with a beta of 1.2 and high R-squared. Its historical returns have a strong relationship with the benchmark, while its beta indicates that its movements have generally been more sensitive than the benchmark's.

A fund can have a relatively high beta but low R-squared if factors beyond the chosen benchmark explain a substantial portion of its movements.

R-squared is most useful as part of a broader fund analysis rather than as a standalone measure.

• Alpha: Indicates performance relative to an appropriate benchmark after accounting for the relevant model assumptions.
• Beta: Indicates sensitivity to benchmark movements.
• Standard deviation: Measures the dispersion of returns and helps assess historical volatility.
• Expense ratio: Shows the recurring operating expenses charged to the scheme.
• Tracking difference: Helps assess how closely a passive fund's returns have followed its benchmark.

For example, a passive index fund with high R-squared but a persistent tracking difference may still require closer examination of its costs and implementation.

You can also review mutual fund ratios to understand how different metrics complement one another.

R-squared can be particularly useful when comparing a fund's behaviour with its stated benchmark.

For a passive fund, a high R-squared may support the expectation that the fund has historically moved closely with its benchmark. For an active fund, R-squared can help determine how much of its historical variation was associated with benchmark movements.

It can also help identify cases where an investor may be comparing a fund against an unsuitable benchmark. A low R-squared may partly reflect a mismatch between the fund's actual investment universe and the selected benchmark rather than a problem with the fund.

R-squared has several limitations that investors should consider.

• Backward-looking: It is calculated from historical data and may change as new observations become available.
• Benchmark-dependent: A poorly chosen benchmark can make the resulting figure less useful.
• No quality assessment: A high R-squared does not indicate good performance.
• No return measurement: It does not show whether the fund generated positive or negative returns.
• No standalone risk assessment: It does not measure overall volatility or downside risk.
• Model-dependent: Results depend on the data frequency, observation period, and regression methodology.
• No prediction guarantee: Historical benchmark relationships may change as portfolio composition or market conditions change.

A high R-squared should therefore never be treated as evidence that a fund will continue to behave similarly in the future.

R-squared can help explain the degree to which a fund's historical movements resemble its benchmark.

For an index fund, a high R-squared is generally consistent with its objective of closely following the benchmark. For an actively managed fund, a high R-squared may indicate that the fund has remained closely aligned with the benchmark despite charging for active management.

However, R-squared should be considered alongside performance, expenses, portfolio composition, investment process, and risk. A low R-squared is not inherently positive because greater divergence can result in either superior or inferior performance.

If you have the fund and benchmark return series, you can calculate the correlation between them and square the result in a simple one-benchmark regression.

For example:

Correlation = 0.80

R² = 0.80² × 100 = 64%

This indicates that 64% of the variation in the fund's returns is explained by the benchmark in the specified model.

For practical fund research, investors can usually obtain R-squared from scheme factsheets or fund-data platforms instead of calculating it manually.

R-squared helps investors understand how much of a fund's historical return variation is explained by movements in its benchmark. It is particularly useful when assessing the relationship between active or passive funds and their chosen benchmarks.

However, R-squared is not a rating of fund quality, risk, or expected returns. Its usefulness depends on the benchmark, data period, and analytical context. Combining it with alpha, beta, standard deviation, costs, tracking difference, and portfolio analysis provides a more complete basis for evaluating a mutual fund.

Last reviewed: October 2026

Mutual funds are subject to market risk. Please read the scheme-related documents carefully before investing.